Model Discrimination with the CMS Detector: a Case Study
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1 Cornell University Floyd R. Newman Laboratory for Elementary-Particle Physics Model Discrimination with the CMS Detector: a Case Study Julia Thom Cornell University (RWTH Aachen) Particle Physics Seminar 3. Physikalisches Institut, RWTH Aachen 5/8/2009 Perelstein, Spethmann, JT, Vaughan, Hallenbek 1 arxiv: [hep-ph], to appear in PRD
2 The Large Hadron Collider (LHC) at CERN 14 TeV pp collisions 2
3 First years of LHC data Begin running with a large number of possible New Physics extensions to the SM Strong limitations on our understanding of first data sample Small statistics Poorly understood detector, immature simulation Primitive triggers, jets, flavor tagging,.. If we see excess over SM predictions, what do we do next to identify the correct New Physics model What are the most powerful model discriminators? How do we deal with the large parameter space of the many NP models? 3
4 This study pick a simple signature with good prospects for clear excess over SM prediction Many New Physics models make a compelling case for pair production of exotic particles decaying to jets + Missing energy (+ X) at the TeV scale Same experimental signature predicted for many of them ( Look-alikes ) Difference in spin of exotic particles Can we exclude classes of NP models based on spin information, assuming realistic conditions? How sensitive are we to exp. effects? Perelstein, Spethmann, JT et al arxiv: [hep-ph], to appear in PRD, 4 See also: Lykken, Spiropulu, Hubisz, et al Phys.Rev.D78:
5 Jets + Missing Energy (+X) at LHC: Why do we think we will see signs of New Physics at the LHC? Plausible extensions to the SM that result in this signature: MSSM Little Higgs with T-parity UED, 5
6 Hierarchy -Problem As the Higgs propagates, it interacts virtually with all particles it can couple to, e.g. Fermions this will contribute to the Higgs mass ( radiative corrections ) H t t Higgs mass can receive enormous corrections proportional to the largest scale in the theory ( Planck Mass, GeV) λ f 2 % t # m H = ("! 2 UV 16$ ) 6
7 One plausible solution: Supersymmetry A symmetry which relates bosons to fermions: We know that a boson loop would contribute to Δm H with opposite sign B 2 $ B 2 " m H = (! +...) 2 UV H 16# λ B Q Boson Q Fermion Fermion Boson This allows for systematic cancellation between Fermion and 2 Boson loop contributions! B =! f Supersymmetry implies that Fermions and Bosons come in super -multiplets, e.g. (t (spin ½), t (spin 0)) = = 7
8 Minimal Supersymmetric Standard Model (MSSM) Minimal extension of SM that realizes Supersymmetry Superpartner for each SM d.o.f., most general SUSYbreaking terms Introduces a discrete R-parity (SM particles are even, superpartners are odd.) 34 new particles [table: S. Martin, hep-ph/ ] 8
9 Generic MSSM predictions All SM states are R-even, superpartners R-odd, so superparticles need to be pair produced, and Lightest SuperPartner (LSP) is stable LSP can be a WIMP dark matter candidate 9
10 Another plausible Solution: Little Higgs Models with T-parity Higgs Mass instability cancelled by particles of the same spin, e.g. spin 1/2 heavy top T Consequence of symmetry structure Have to introduce T-parity to satisfy exp. constraints T-odd partner for each SM particle (T-quarks, T-leptons) Lightest T-odd particle is stable, spin-1 heavy photon WIMP DM candidate T H t T H 10 [Carena, Hubisz, MP, Verdier, hep-ph/ , PRD75:091701]
11 Summary MSSM vs.lht MSSM: boson cancels fermion Squarks have spin 0 dark matter candidate χ 0 has spin 1/2 Same for UED Little Higgs with T-parity: boson cancels boson T-quarks have spin 1/2 dark matter candidate B H has spin 1 T, T,, B H T, Look-alike models T,, B H Dominant Production at LHC: jets and missing energy 11
12 Similarly, many other extensions of the SM at the EWK scale possible Light Higgs and mirror particles at TeV scale Lightest New Particle (LNP) is stable and weakly interacting Same LHC phenomenology: pair production of new states which then decay down to LNPs and SM states jets, MET (and leptons) in the detector 12
13 What can we do to distinguish between them? Complete spectrum and coupling strengths hard to measure (ILC) Determine spins of new particles X through angular correlations between decay products, but notoriously difficult 13
14 Pair Production of exotic particles Angular distribution of decay products carries spin information. Total event rate provides information too (fermions have more DOF than scalars). more central UED less central For example: Jets from spin-0 squarks more central (cons.of ang.mom.) SUSY, LHT COM frame unknown: need boost invariant variables. pseudorapidity Δη or 14
15 Squark Pair Production Strong dependence of angular distributions on gluino mass Heavier gluino more favorable SUSY LHT, UED Shown are quark-initiated processes only, in parton COM frame 15
16 Side note: spin correlations in cascade decay Barr hep-ph/ , Almost all existing proposals to measure spin rely on cascade decays E.g. use invariant mass of lepton and jet, since it depends on angle between q and l in χ 2 0 rest frame Studies so far ignore backgrounds and are done at generator level problems: low rates and combinatorics 16
17 Jets + MET: experimental challenges The Signal and its Backgrounds Experience from the Tevatron Plans for the LHC 17
18 Jets + MET: exp. signature LNP escapes the detector and results in missing transverse energy (MET) Signature: at least 2 jets, large MET and 0 leptons Backgrounds: Z(νν)+jets, W+jets, ttbar Neutrinos give MET Most have associated leptons QCD MET from mis-measurement Detector/Instrumental effects Dibosons SUSY 18 (fb)
19 Physics Backgrounds, Tevatron Experience QCD: MET from mis-measurement QCD control region used to understand and model jet background correctly, esp. high MET tails 19
20 SUSY (and LHT) at Tevatron Roughly excluding m(squark)<400 GeV, M(T-quark)<400 GeV in direct searches 20
21 Projections for the LHC Example: Atlas jet+met analysis m(squark)=600 GeV, m(gluino)=700 GeV Require jets, large MET and 0 leptons Note that signal here is optimized benchmark point 21
22 This Study Given the experimental challenge, can we use measurements of angular jet correlations to tell the spin of the underlying particle (squark or T-quark or..) and thus exclude certain classes of NP models? How to deal with huge parameter space of each model? 22
23 This study As a case study, we assume MSSM with certain parameter choice is true ( mock-data ) Assume that MSSM squark pair-production dominates and that direct 2-body decays causes excess in 2 hard jets + large MET signature try to fit with a look-alike wrong model, and scan over its parameter space Here: look-alike is Little Higgs Model Use jet distributions as model discriminators How much data would we need to exclude the wrong model? How sensitive are we to experimental effects? 23
24 Our data point the following MSSM parameters create chosen data signature Parameter choice motivated by creating simple signature (pair production of 1st generation squarks) Gluino relatively heavy, different than LM1 (SU3) benchmark point (light Gluino)! Cross-section is ~5 pb 24
25 Analysis Cuts Guided by CMS jets+met SUSY analysis: At least 2 jets Pt jet1 >150 GeV, Pt jet2 >100 GeV η jet1 <1.7&& η jet2 <1.7 MET>300GeV (corrected for jets) No identified leptons in the event 25
26 SM Backgrounds Selected SM background events for 2fb -1 after cuts signal Z(νν)+jets (W->νl)+2 jets (W->ντ)+1jet ttbar Total bkg Note: QCD background not considered, since simulation will not get this right at all Even though: S/N only ~ 1-2 heavy gluino results in low signal cross-section We kept this non-optimal MSSM point as a generic (and realistic) case 26
27 Fitting with the wrong spin model Pick 10 Observables that are sensitive to angular correlations Scan LHT parameter space to find the best fit point. LHT ruled out only if that point is ruled out. Each point in the scan requires MC simulation, efficient and realistic simulation is the key using parametrized toy MC PGS ( pretty good simulation ) tuned for CMS detector 27
28 Simulation Setup Squark/T-quark prod.&decay (model input) MadGraph/ MadEvent Showering and hadronization (Pythia) Tuned CMS toy simulation PGS Full CMS simulation and event reco Calibration Used to scan LHT parameter space, generate background samples 28
29 Tuned CMS toy simulation For jet+met signature the main issue are jet energies PGS jet distributions tuned by comparing to Full CMS simulation for MSSM data point and one LHT sample (100k events) Straightforward for high-pt jets (>100 GeV) 29
30 corrections applied to PGS generated jet energy: From CMS note 2006/036 30
31 Jet energy (MSSM) before PGS jet energy scaling after PGS jet energy scaling CMS full simulation PGS output Lead jet pt Lead jet pt jet pt jet pt MET MET 31
32 Summary PGS toy simulation Validated using MSSM data sample and 1 LHT sample 100k events each Find very good agreement after tuning Vary T-quark mass and heavy photon mass (125 points in parameter space) number of events in each sample correspond to 10 fb -1 PGS used to generate the background samples again cross-checked with Full Simulation results 32
33 Observables Pick variables sensitive to angular correlations Found set of 10 (correlated) quantities 33
34 10 Observables 5 Asymmetries and ratios based on angular correlations Use large bins of distributions for robustness Use ratios of counts in different bins Additionally: <H T >, <MET>, <p t >, <η> Cross section Calculated from total number of signal and background events after cuts 34
35 Asymmetries, Ratios Beamline asymmetry (alignment of 2 leading jets with the beam pipe) BA = N + " N " N + + N " N + (N - ) is number of events with 2 lead jet η 1 η 2 >0 (η 1 η 2 <0) Directional asymmetry (alignment of jets with each other) let θ be the angle between the two leading jets. N + (N - ) is number of events with cos θ positive (negative) Transverse Momentum Asymmetry The ratio N + /N - of the number of jets with pt larger than the average and the number of jets with pt smaller than the average Transverse Momentum Bin Ratios Distribute jets into 3 pt bins and define bin count ratios R 1 = N 2 /N 1 and R 2 = N 3 /N 1 35
36 Asymmetries Δη jj smaller for MSSM, η 1 η 2 >0 more often Beam Line (and Directional) asymmetry more positive for MSSM UED more central less central 36
37 example distributions at one LH point (M Q = 500, M B =100 GeV) data (MSSM) 2fb -1 Hist: LHT model Cosine of the angle between two hardest jets Includes the background contributions 37
38 Observables: p t Different p T spectra of jets depending on squark/t-quark masses and angular distributions e.g. for same jet energy, central jets have higher p T 38
39 data (MSSM) Hist: LHT model data (MSSM) Hist: LHT model 39
40 Syst.Uncertainties Jet energy and jet η uncertainty estimated using parameterizations from CMS TDR1 Estimated systematic on the cross section measurement using luminosity uncertainty, pythia factorization and renormalization scale, total ~30% Note that we don t yet include systematic uncertainties on shapes - potentially large uncertainty 40
41 Statistical Analysis 1. Compute measured value of observables using data 2. For each LHT point in the scan, we compute the expected central values 3. Use standard χ 2 technique to estimate quality of fit between expected and measured values Assume observables to be gaussian distributed with stat. and syst errors Correlation matrix obtained from MC samples 4. Can convert each χ 2 value into probability that disagreement between model and data is the result of fluctuation 41
42 Results Expressed as Exclusion Plots For each of our scan points, at which confidence level can we exclude the look-alike model from our data point? 42
43 Exclusion Plots Combined fit to 10 observables 200pb -1 Y-axis: heavy photon (B H ) mass X-axis: heavy T-quark mass best fit Green: 4σ deviation between data and LHT model Light blue: 3σ deviation dark blue: 2σ deviation, etc.. 43
44 Exclusion Levels Combined fit to 10 observables 200pb pb -1 Y-axis: heavy photon (B H ) mass X-axis: heavy T-quark mass 1fb -1 2fb -1 E.g best fit point: less than 1 σ deviation from the data 44
45 How dependent on individual observables? 2fb -1 2fb -1 Exclusion levels without cross-section info..without <MET> and <H T > info 45
46 Correlation matrix Correlation between variables change χ 2 values of combined fit considerably Estimate correlations from the MC using bootstrapping method Example: MSSM plus BKGD data (2fb -1 ) 46
47 Determine correlations Ideally generate every point in LH parameter space ~1000x to determine correlation between variables. Takes too long. Instead, subdivide each sample into small samples and determine correlation pick 20 sets with replacement and repeat 10,000x Get distribution of correlation matrix values plus error Correlation between H t and MET For 2 fb-1 of SUSY plus BKGD events 20 subsamples and 10,000 repeats 47
48 Summary Have developed the machinery to study exclusion levels of a New Physics model, given a data signal, backgrounds, and systematic uncertainties. Based on angular correlations of decay products Scans over parameter space of the model in question First study of its kind Presented case study of a specific MSSM data signal and LHT look-alike Uses generic (=non-optimal) MSSM point as truth made a few simplifications: Jets + MET signature assumed dominant Backgrounds, toy MC, etc 48
49 Conclusions Difficult task but not impossible: jet angular correlations washed out by background and jet reconstruction uncertainty Will for example need considerable amount of data (>2fb -1 ) to reliably exclude large areas of wrong-spin model Even then, need to combine information from many observables 49
50 Lessons and Extensions Scanning parameters of the candidate model is crucial Improvements needed to make this study fully realistic shapes of distributions assumed to be exact Better/complete background estimates Cross-check results with CMS FastSim Further studies Sensitivity to masses in the correct model? Repeat for signature with leptons Fit to UED and other models 50
51 Backup Slides 51
52 Backgrounds Size of each sample corresponds to 2fb -1 of LHC data Listing dominant backgrounds EXCEPT QCD jet background with mis-measured MET 52
53 Instrumental Backgrounds Sources: Calorimeter noise, cosmic rays and beam halo muons showering hard in calorimeter From CDF experience: lengthy process to understand MET distribution 53
54 Comparison to jet+met TDRII analysis For similar cuts TDRII jet+met analysis quotes S/N=26 (factor 10 higher LM1 SUSY signal x-section because of light gluino) 54
55 Main systematic: varying the pythia renormalization and factorization scale Down MSSM LHT BLA 0.149± ±0.006 DA ± ±0.009 Mid BLA 0.147± ±0.006 DA ± ±0.009 Up BLA 0.159± ±0.006 DA ± ±0.009 This is a systematic effect of the order of ±0.02 (we don t know the correct factorization scale) 55
56 p T Φ θ p T : Components momentum transverse to the beam axis θ: Polar angle Φ: Azimuthal angle 56
57 Pseudorapidity η=0 η=1 CMS Detector: η=2 57
58 Before cuts After cuts CMS full simulation PGS output Lead jet pt Lead jet pt jet pt jet pt MET MET 58
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